Question

You are shopping for a King & Queen size mattress, each of which are shaped like a rectangle. The Queen is 16 inches longer than it is wide. The King is 20 inches wider than the Queen, but has the same length. The area of the King-sized mattress is 1,600 in² larger than the Queen. Find the Area of both mattresses.

Answer 1

Answer:

Let width of the queen matress be x in

Its length = (x + 16) in

Also, width of king matress = (x + 20) in

And, length of king matress = (x + 16) in

Area of queen matress = x(x + 20) = x² + 20x in²

Area of king matress = (x + 16)(x + 20) = x² + 36x + 320 in²

So, we have

x² + 20x + 1600 = x² + 36x + 320

=> 16x = 1280

=> x = 80

So,

area of queen matress = 80² + 20×80 = 6400 + 1600 = 8000 in²

area of king matress = 80² + 36×80 + 320 = 6400 + 2880 + 320 = 9600 in²